2008 AMC12 A #12

A function \(f\) has domain \([0, \; 2]\) and range \([0, \; 1]\). (The notation \([a, \; b]\) denotes \( \{ x\; : \; a \le x \le b \}\).) What are the domain and range, respectively, of the function \(g\) defined by \(g(x)=1-f(1+x)\) ?

(A) \([-1, \; 1 ], \; [-1, \; 0]\)

(B) \([-1, \; 1 ], \; [0, \; 1]\)

(C) \([0, \; 2 ], \; [-1, \; 0]\)

(D) \([1, \; 3 ], \; [-1, \; 0]\)

(E) \([1, \; 3], \; [0, \; 1]\)

정답 (B)